uspsa.org, for action type matches.
idpa.com, for defensive type matches.
NRA action pistol, also known as the Bianchi Cup type match.
Steel Challenge matches, also at the uspsa.org web site.
Silhouette matches (steel knockdown targets shaped like critters).
Bowling pin matches.
Just do web searches for the ones above that don't have web site links, to get started.
So many choices, so little time.